On the dynamics of 3d electrified falling films

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URI: http://hdl.handle.net/10902/24534
ISSN: 1553-5231
ISSN: 1078-0947
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Autoría
He, Jiao; Granero Belinchón, RafaelAutoridad Unican
Fecha
2021-09
Derechos
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version Discrete and Continuous Dynamical Systems - Series A, 41 (9), 4041 - 4064 is available online at: http://dx.doi.org/10.3934/dcds.2021027
Publicado en
Discrete and Continuous Dynamical Systems - Series A, 41 (9), 4041 - 4064
Editorial
American Institute of Mathematical Sciences
Palabras clave
Kuramoto-Sivashinsky equation
Global wellposedness
Analyticity
Global attractor
Upper bound on the number of spatial oscillations
Resumen/Abstract
In this article, we consider a non-local variant of the KuramotoSivashinsky equation in three dimensions (2D interface). Besides showing the global wellposedness of this equation we also obtain some qualitative properties of the solutions. In particular, we prove that the solutions become analytic in the spatial variable for positive time, the existence of a compact global attractor and an upper bound on the number of spatial oscillations of the solutions. We observe that such a bound is particularly interesting due to the chaotic behavior of the solutions.
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